Problem: $ \left(\dfrac{100}{49}\right)^{-\frac{3}{2}}$
Solution: $= \left(\dfrac{49}{100}\right)^{\frac{3}{2}}$ $= \left(\left(\dfrac{49}{100}\right)^{\frac{1}{2}}\right)^{3}$ To simplify $\left(\dfrac{49}{100}\right)^{\frac{1}{2}}$ , figure out what goes in the blank: $\left(? \right)^{2}=\dfrac{49}{100}$ To simplify $\left(\dfrac{49}{100}\right)^{\frac{1}{2}}$ , figure out what goes in the blank: $\left({\dfrac{7}{10}}\right)^{2}=\dfrac{49}{100}$ so $ \left(\dfrac{49}{100}\right)^{\frac{1}{2}}=\dfrac{7}{10}$ So $\left(\dfrac{49}{100}\right)^{\frac{3}{2}}=\left(\left(\dfrac{49}{100}\right)^{\frac{1}{2}}\right)^{3}=\left(\dfrac{7}{10}\right)^{3}$ $= \left(\dfrac{7}{10}\right)\cdot\left(\dfrac{7}{10}\right)\cdot \left(\dfrac{7}{10}\right)$ $= \dfrac{49}{100}\cdot\left(\dfrac{7}{10}\right)$ $= \dfrac{343}{1000}$